The survival probability for critical spread-out oriented percolation above 4+14+1 dimensions. II. Expansion
نویسندگان
چکیده
منابع مشابه
The survival probability for critical spread - out oriented percolation above 4 + 1 dimensions . II . Expansion
We derive a lace expansion for the survival probability for critical spread-out oriented percolation above 4+1 dimensions, i.e., the probability θn that the origin is connected to the hyperplane at time n, at the critical threshold pc. Our lace expansion leads to a nonlinear recursion relation for θn, with coefficients that we bound via diagrammatic estimates. This lace expansion is for point-t...
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We consider critical spread-out oriented percolation above 4+1 dimensions. Our main result is that the extinction probability at time n (i.e., the probability for the origin to be connected to the hyperplane at time n but not to the hyperplane at time n + 1) decays like 1/Bn2 as n →∞, where B is a finite positive constant. This in turn implies that the survival probability at time n (i.e., the ...
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ژورنال
عنوان ژورنال: Annales de l'Institut Henri Poincare (B) Probability and Statistics
سال: 2007
ISSN: 0246-0203
DOI: 10.1016/j.anihpb.2006.09.002